This is a pilot, phase I, placebo controlled clinical trial of short-term high-dose thyroid hormone to promote remyelination in MS. Permanent clinical disability in MS is likely caused by the neuronal damage and degeneration that follows recurrent demyelination with progressive failure of remyelination. Thyroid hormone (TH) is required for central nervous system (CNS) myelination during development, and CNS remyelination in animal models of MS, a process similar to developmental myelination, has also been found to be promoted by TH. This study will ascertain the safety, tolerability and maximum tolerated dose of TH in people with MS, explore for a signal of treatment efficacy and mechanism, and optimize procedures for a full scale clinical trial to evaluate the efficacy of pulsed TH for promotion of remyelination in MS.